Here's my code,
data1 = Data.objects.filter(...).annotate(Max('receiver')).order_by('-receiver__max')
data2 = Data.objects.filter(...).annotate(Max('sender')).order_by('-sender__max')
How can I combine these 2 queries in just one single Query?
You should be able to combine it quite nicely, and if you're only interested in the max values then there's no need to also order_by. You should just be able to do;
data = Data.objects.filter(...).annotate(Max('receiver'), Max('sender'))
Which should return something like;
{'receiver__max': 10, 'sender__max': 12}